Affiliations: [a] School of Mathematics and Information Science, North Minzu University, Yinchuan, China
| [b] Department of Computer Science and Technology, Tongji University, Shanghai, China
Correspondence:
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Corresponding author. Renxia Wan, School of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia, 750021, China. E-mail: wanrx1022@nmu.edu.cn.
Abstract: Multi-granulation decision-theoretic rough set effectively combines Bayesian decision approaches with multi-granulation rough set theory, and provides an important theoretical framework for studying rough set. In this paper, we explore several extensional models of multi-granulation decision-theoretic rough sets under the normal distribution of the decision loss function. Using the 3σ rule of normal distribution, we transform the decision loss of the multi-granulation decision-theoretic rough set into a set of interval values. We construct the upper and lower approximations from the optimistic, weakly optimistic, pessimistic, weakly pessimistic, optimistic-pessimistic, weakly optimistic-pessimistic, pessimistic-optimistic, and weakly pessimistic-optimistic viewpoints, and provide the decision rules of the proposed rough set models. The work in this paper brings the decision behavior based on a multi-granulation decision-theoretic rough set closer to the actual situation.
Keywords: Loss function, normal distribution, interval value, multi-granulation decision-theoretic rough set
